Finite Group Databasebeta

← #7626774

Subgroups — #7626774

Order 512.

6376 conjugacy classes of subgroups.

The subgroup lattice has 1429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic
2#34505C214yesmaximal, complemented
3#34490C212yesmaximal, complemented
4#34490C214yesmaximal, complemented
5#34488C212yesmaximal, complemented
6#34475C212yesmaximal, complemented
7#34475C212yesmaximal, complemented
8#34465C212yesmaximal, complemented
9#34463C212yesmaximal, complemented
10#34459C214yesmaximal, complemented
11#34455C214yesmaximal, complemented
12#34445C214yesmaximal, complemented
13#34390C212yesmaximal
14#34389C212yesmaximal, complemented
15#34334C212yesmaximal, complemented
16#34314C212yesmaximal, complemented
17#34297C214yesmaximal, complemented
18#34286C212yesmaximal, complemented
19#34262C212yesmaximal, complemented
20#34254C212yesmaximal, complemented
21#34241C211yesmaximal, characteristic
22#34234C212yesmaximal
23#34221C211yesmaximal, characteristic, complemented
24#34215C212yesmaximal, complemented
25#34149C211yesmaximal, characteristic
26#34145C211yesmaximal, characteristic, complemented
27#34128C211yesmaximal, characteristic, complemented
28C4×#541C212yesmaximal, complemented
29C2×#2320C211yesmaximal, characteristic, complemented
30#3523C4132yescomplemented
31C2×#557C2211yescharacteristic
32C2×#557C2212yes—
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#556C2212yes—
36C2×#552C2212yes—
37C2×#552C2214yes—
38C2×D4×Q8C2212yes—
39C2×D4×Q8C2211yescharacteristic
40C2×#541C2212yes—
41C2×#541C2214yes—
42C2×#533C2212yes—
43C2×#533C2211yescharacteristic
44C2×#529C2212yes—
45C2×#529C2211yescharacteristic
46C2×#519C2212yes—
47C22×C4×Q8C2211yescharacteristic
48#2383C2214yes—
49#2383C2214yes—
50#2382C2214yes—
51#2382C2214yes—
52#2382C2214yes—
53#2382C2214yes—
54#2381C2214yes—
55#2381C2214yes—
56#2381C2214yes—
57#2379C2214yes—
58#2378C2214yes—
59#2378C2214yes—
60#2373C2214yes—
61#2373C2212yes—
62#2373C2212yes—
63#2373C2214yes—
64#2373C2214yes—
65#2373C2214yes—
66#2373C2214yes—
67#2372C2212yes—
68#2371C2212yes—
69#2371C2212yes—
70#2371C2212yes—
71#2371C2214yes—
72#2371C2214yes—
73#2370C2214yes—
74#2370C2212yes—
75#2370C2214yes—
76#2370C2214yes—
77#2370C2214yes—
78#2370C2212yes—
79#2369C2214yes—
80#2369C2212yes—
81#2368C2214yes—
82#2368C2214yes—
83#2368C2211yescharacteristic
84#2368C2212yes—
85#2368C2212yes—
86#2368C2212yes—
87#2368C2212yes—
88#2368C2212yes—
89#2368C2211yescharacteristic
90#2368C2214yes—
91#2368C2214yes—
92#2365C2212yes—
93#2365C2212yes—
94#2365C2212yes—
95#2364C2211yescharacteristic
96#2364C2212yes—
97#2364C2211yescharacteristic
98#2362C2212yes—
99#2362C2212yes—
100#2360C2212yes—
101#2360C2212yes—
102#2360C2212yes—
103#2360C2212yes—
104#2359C2214yes—
105#2359C2212yes—
106#2359C2212yes—
107#2359C2214yes—
108#2356C2212yes—
109#2356C2214yes—
110#2356C2214yes—
111#2356C2214yes—
112#2356C2212yes—
113#2356C2214yes—
114#2356C2214yes—
115#2356C2214yes—
116#2355C2212yes—
117#2355C2214yes—
118#2355C2214yes—
119#2355C2214yes—
120#2355C2214yes—
121#2355C2214yes—
122#2355C2212yes—
123#2353C2214yes—
124#2353C2214yes—
125#2352C2212yes—
126#2352C2212yes—
127#2351C2212yes—
128#2351C2212yes—
129Q8×C4⋊C4C2212yes—
130#2349C2214yes—
131D4×C4⋊C4C2212yes—
132#2347C2212yes—
133#2347C2214yes—
134#2346C2214yes—
135#2346C2212yes—
136#2344C2211yescharacteristic
137#2344C2212yes—
138#2344C2211yescharacteristic
139#2344C2212yes—
140#2343C2214yes—
141#2343C2214yes—
142#2343C2214yes—
143#2343C2214yes—
144#2343C2214yes—
145#2343C2214yes—
146#2343C2214yes—
147Q8×C22⋊C4C2211yescharacteristic
148Q8×C22⋊C4C2212yes—
149Q8×C22⋊C4C2211yescharacteristic
150Q8×C22⋊C4C2212yes—
151#2337C2214yes—
152#2337C2212yes—
153#2336C2214yes—
154#2336C2214yes—
155#2336C2214yes—
156#2336C2214yes—
157#2336C2214yes—
158#2336C2214yes—
159#2336C2214yes—
160#2336C2214yes—
161#2336C2212yes—
162#2334C2214yes—
163#2334C2214yes—
164#2334C2214yes—
165#2334C2214yes—
166#2334C2214yes—
167#2334C2214yes—
168#2334C2214yes—
169#2332C2214yes—
170#2332C2214yes—
171#2331C2214yes—
172#2331C2214yes—
173#2331C2212yes—
174#2331C2214yes—
175#2331C2214yes—
176#2330C2212yes—
177#2330C2214yes—
178#2330C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2327C2212yes—
184#2327C2212yes—
185#2323C2212yes—
186#2323C2212yes—
187#2322C2214yes—
188#2322C2214yes—
189#2320C2211yescharacteristic
190#2320C2212yes—
191#2320C2212yes—
192#2320C2212yes—
193#2320C2212yes—
194#2320C2214yes—
195#2320C2211yescharacteristic
196#2320C2211yescharacteristic
197#2320C2211yescharacteristic
198#2320C2212yes—
199#2320C2214yes—
200#2320C2214yes—
201#2320C2214yes—
202#2320C2214yes—
203#2320C2212yes—
204#2320C2212yes—
205#2318C2214yes—
206#2318C2214yes—
207#2317C2214yes—
208#2317C2212yes—
209#2314C2212yes—
210#2314C2214yes—
211#2310C2212yes—
212C4×C4⋊Q8C2212yes—
213C4×#125C2212yes—
214C4×#125C2214yes—
215C4×#125C2214yes—
216C4×#125C2214yes—
217C4×#126C2214yes—
218C4×#126C2214yes—
219C4×#126C2214yes—
220C4×C22⋊Q8C2212yes—
221C4×C22⋊Q8C2212yes—
222C4×C22⋊Q8C2212yes—
223C4×C22⋊Q8C2212yes—
224C4×#123C2214yes—
225#2298C2212yes—
226#2298C2214yes—
227#2296C2212yes—
228#2296C2212yes—
229#2295C2212yes—
230#2295C2212yes—
231#2295C2214yes—
232#2295C2212yes—
233#2295C2214yes—
234#2295C2212yes—
235#2295C2212yes—
236#2295C2214yes—
237C2×#391C2212yes—
238C2×#391C2212yes—
239C2×#389C2212yes—
240#2290C2212yes—
241#2290C2212yes—
242C2×#387C2214yes—
243#2283C2212yes—
244#2283C2211yescharacteristic
245C2×#383C2212yes—
246C2×#382C2212yes—
247#2276C2212yes—
248#2275C2214yes—
249#2274C2214yes—
250#2274C2212yes—
251C42×Q8C2212yes—
252C42×Q8C2212yes—
253C42×D4C2212yes—
254C4×#117C2212yes—
255C4×#117C2211yescharacteristic
256C4×#117C2212yes—
257C4×#117C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259C2×#376C2211yescharacteristic
260C23×Q8C2312yes—
261C23×Q8C2311yescharacteristic
262#557C2×C4116yescomplemented
263#557C2×C4116yescomplemented
264#557C2×C4132yescomplemented
265#556C2×C4116yescomplemented
266#556C2×C4132yescomplemented
267#552C2×C4132yescomplemented
268#552C2×C4164yescomplemented
269D4×Q8C2×C4132yescomplemented
270D4×Q8C2×C4116yescomplemented
271#541C2×C4132yescomplemented
272#541C2×C4164yescomplemented
273#533C2×C4132yescomplemented
274#533C2×C4116yescomplemented
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281#529C2×C4132yes—
282#529C2×C4116yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2312yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2311yescharacteristic
294C2×#125C2314yes—
295C2×#125C2312yes—
296C2×#125C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2312yes—
299C2×#123C2314yes—
300C2×#123C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2311yescharacteristic
308C2×C22⋊Q8C2312yes—
309C2×#121C2311yescharacteristic
310#519C2×C4132yescomplemented
311C2×C4×Q8C2×C4116yescomplemented
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2314yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2314yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×#117C2311yescharacteristic
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2311yescharacteristic
347C2×#117C2314yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C2×#117C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C42C2312yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362C22×C42C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2312yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2312yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2312yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2312yes—
391#391C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#388C2312yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2312yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2312yes—
444#388C2312yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2312yes—
449#388C2312yes—
450#388C2312yes—
451#388C2314yes—
452#388C2312yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2312yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2312yes—
484#387C2312yes—
485#387C2314yes—
486#387C2312yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2312yes—
513#387C2312yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2312yes—
537#386C2312yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#386C2312yes—
542#386C2312yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2312yes—
555#385C2312yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2312yes—
560#385C2314yes—
561#384C2312yes—
562#384C2314yes—
563#384C2314yes—
564#383C2312yes—
565#383C2312yes—
566#383C2314yes—
567#383C2314yes—
568#383C2314yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#383C2314yes—
573#383C2312yes—
574#383C2312yes—
575#383C2314yes—
576#383C2312yes—
577#382C2312yes—
578#382C2312yes—
579#382C2312yes—
580#382C2314yes—
581#382C2314yes—
582#382C2314yes—
583#382C2314yes—
584#382C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2314yes—
588#382C2312yes—
589#382C2312yes—
590#382C2314yes—
591#382C2314yes—
592#382C2312yes—
593#381C2314yes—
594#381C2314yes—
595#381C2312yes—
596#381C2312yes—
597#381C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2311yescharacteristic
605#380C2311yescharacteristic
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2311yescharacteristic
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2311yescharacteristic
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2312yes—
700#376C2311yescharacteristic
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2311yescharacteristic
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710#376C2314yes—
711#376C2314yes—
712#376C2314yes—
713#376C2314yes—
714#376C2314yes—
715#376C2312yes—
716#376C2312yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C2×#95C2314yes—
720C2×#95C2312yes—
721C2×#95C2314yes—
722C2×#95C2314yes—
723C2×#95C2311yescharacteristic
724C2×#95C2311yescharacteristic
725C2×#95C2312yes—
726C43C2314yes—
727C43C2314yes—
728C43C2312yes—
729C43C2312yes—
730C22×Q8—44no—
731C22×Q8—44no—
732C22×Q8—44no—
733C22×Q8C22×C418yes—
734C22×Q8C22×C4116yes—
735C22×Q8C2411yescharacteristic
736C22×Q8C2412yes—
737C22×Q8C2411yescharacteristic
738C22×Q8C2411yescharacteristic
739C22×Q8C2412yes—
740C22×Q8C2412yes—
741C22×Q8C2414yes—
742C22×D4C2412yes—
743C22×D4C2411yescharacteristic
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2411yescharacteristic
757C4⋊Q8C22×C418yes—
758C4⋊Q8C22×C4116yes—
759C4⋊Q8C22×C418yes—
760C4⋊Q8C22×C4116yes—
761C4⋊Q8C22×C4116yes—
762C4⋊Q8C22×C4132yes—
763#126C22×C4132yes—
764#126C22×C4116yes—
765#126C22×C4132yes—
766#126C22×C4132yes—
767#126C22×C4132yes—
768#125C22×C418yes—
769#125C22×C4116yes—
770#125C22×C4132yes—
771#125C22×C4116yes—
772#125C22×C4132yes—
773#125C22×C4132yes—
774#125C22×C4132yes—
775#125C22×C4116yes—
776#125C22×C4132yes—
777#124C22×C418yes—
778#124C22×C4116yes—
779#123C22×C4132yes—
780#123C22×C4116yes—
781C22⋊Q8C22×C418yes—
782C22⋊Q8C22×C4116yes—
783C22⋊Q8C22×C4116yes—
784C22⋊Q8C22×C4132yes—
785C22⋊Q8C22×C4116yes—
786C22⋊Q8C22×C4132yes—
787C22⋊Q8C22×C4116yes—
788C22⋊Q8C22×C4132yes—
789#121C22×C418yes—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8C22×C418yes—
797C4×Q8C22×C418yes—
798C4×Q8C22×C4116yes—
799C4×Q8C22×C418yes—
800C4×Q8C22×C418yes—
801C4×Q8C22×C4116yes—
802C4×Q8C22×C4116yes—
803C4×Q8C22×C4132yes—
804C4×Q8C22×C4116yes—
805C4×Q8C22×C4116yes—
806C4×Q8C22×C4132yes—
807C4×Q8C22×C4116yes—
808C4×Q8C22×C418yes—
809C4×Q8C22×C4116yes—
810C4×Q8C22×C4116yes—
811C4×Q8C22×C4116yes—
812C4×D4—28no—
813C4×D4—48no—
814C4×D4—44no—
815C4×D4C22×C4116yes—
816C4×D4C22×C4132yes—
817C4×D4C22×C418yes—
818C4×D4C22×C4116yes—
819#117—24no—
820#117—28no—
821#117—44no—
822#117—42no—
823#117—44no—
824#117—44no—
825#117C22×C4116yes—
826#117C22×C4132yes—
827#117C22×C4116yes—
828#117C22×C4132yes—
829#117C22×C4132yes—
830#117C22×C4116yes—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—44no—
833C2×C4⋊C4—48no—
834C2×C4⋊C4C22×C418yes—
835C2×C4⋊C4C22×C4116yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2411yescharacteristic
919C2×C42—44no—
920C2×C42—44no—
921C2×C42—44no—
922C2×C42C22×C418yes—
923C2×C42C22×C4116yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2411yescharacteristic
978#95C2414yes—
979#95C2411yescharacteristic
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048C24C2512yes—
1049C24C2511yescharacteristic
1050C2×Q8—24no—
1051C2×Q8—24no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—42no—
1058C2×Q8—44no—
1059C2×Q8—416no—
1060C2×Q8—432no—
1061C2×Q8C23×C414yes—
1062C2×Q8C23×C414yes—
1063C2×Q8C23×C418yes—
1064C2×Q8C23×C418yes—
1065C2×Q8C23×C414yes—
1066C2×Q8C23×C418yes—
1067C2×Q8C23×C4116yes—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—42no—
1071C2×D4C23×C418yes—
1072C2×D4C23×C414yes—
1073C22×C4—24no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—28no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4C23×C418yes—
1103C22×C4C23×C414yes—
1104C22×C4C23×C414yes—
1105C22×C4C23×C418yes—
1106C22×C4C23×C414yes—
1107C22×C4C23×C418yes—
1108C22×C4C23×C4116yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2514yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4C23×C418yes—
1169C4⋊C4C23×C414yes—
1170C4⋊C4C23×C418yes—
1171C4⋊C4C23×C414yes—
1172C4⋊C4C23×C418yes—
1173C4⋊C4C23×C418yes—
1174C4⋊C4C23×C418yes—
1175C4⋊C4C23×C4116yes—
1176C4⋊C4C23×C418yes—
1177C4⋊C4C23×C418yes—
1178C4⋊C4C23×C4116yes—
1179C4⋊C4C23×C418yes—
1180C4⋊C4C23×C4116yes—
1181C4⋊C4C23×C4116yes—
1182C4⋊C4C23×C418yes—
1183C4⋊C4C23×C4116yes—
1184C4⋊C4C23×C418yes—
1185C4⋊C4C23×C414yes—
1186C4⋊C4C23×C418yes—
1187C4⋊C4C23×C418yes—
1188C4⋊C4C23×C4116yes—
1189C4⋊C4C23×C414yes—
1190C4⋊C4C23×C4116yes—
1191C4⋊C4C23×C4116yes—
1192C4⋊C4C23×C4116yes—
1193C4⋊C4C23×C4116yes—
1194C4⋊C4C23×C418yes—
1195C22⋊C4—22no—
1196C22⋊C4—24no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4C23×C418yes—
1210C22⋊C4C23×C418yes—
1211C22⋊C4C23×C4116yes—
1212C22⋊C4C23×C418yes—
1213C22⋊C4C23×C4116yes—
1214C22⋊C4C23×C418yes—
1215C22⋊C4C23×C4116yes—
1216C22⋊C4C23×C418yes—
1217C22⋊C4C23×C4116yes—
1218C22⋊C42−1+414yes—
1219C42—24no—
1220C42—28no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—42no—
1227C42—42no—
1228C42—42no—
1229C42—44no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—42no—
1234C42—44no—
1235C42—42no—
1236C42—42no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—42no—
1243C42—42no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—42no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42C23×C418yes—
1255C42C23×C414yes—
1256C42C23×C418yes—
1257C42C23×C414yes—
1258C42C23×C414yes—
1259C42C23×C418yes—
1260C42C23×C418yes—
1261C42C23×C414yes—
1262C42C23×C4116yes—
1263C42C23×C4116yes—
1264C42C23×C4116yes—
1265C42C23×C4116yes—
1266C42C23×C418yes—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23C24×C414yes—
1276C23C24×C412yes—
1277C23C2×2−1+412yes—
1278C23#58512yes—
1279C23C2611yescharacteristic
1280Q8—28no—
1281Q8—28no—
1282Q8—216no—
1283Q8—416no—
1284Q8—48no—
1285Q8—44no—
1286Q8—48no—
1287D4—216no—
1288D4—44no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—28no—
1315C2×C4—216no—
1316C2×C4—28no—
1317C2×C4—216no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—44no—
1352C2×C4—48no—
1353C2×C4—416no—
1354C2×C4—84no—
1355C2×C4—84no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4—84no—
1359C2×C4—164no—
1360C2×C4C24×C412yes—
1361C2×C4C24×C414yes—
1362C2×C4C24×C412yes—
1363C2×C4C24×C412yes—
1364C2×C4C24×C414yes—
1365C2×C4C24×C418yes—
1366C2×C4C24×C414yes—
1367C2×C4C24×C414yes—
1368C2×C4C24×C414yes—
1369C2×C4C24×C412yes—
1370C2×C4C24×C412yes—
1371C2×C4C24×C414yes—
1372C2×C4C24×C414yes—
1373C2×C4C24×C418yes—
1374C2×C4C24×C412yes—
1375C2×C4C2×2−1+414yes—
1376C2×C4#58514yes—
1377C22—22no—
1378C22—22no—
1379C22—24no—
1380C22—24no—
1381C22—24no—
1382C22—24no—
1383C22—24no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22C4×2−1+414yes—
1389C22C25×C411yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22C2×#58512yes—
1392C22C2×#58511yescharacteristic
1393C222−1+612yes—
1394C4—24no—
1395C4—22no—
1396C4—24no—
1397C4—24no—
1398C4—28no—
1399C4—22no—
1400C4—24no—
1401C4—22no—
1402C4—24no—
1403C4—24no—
1404C4—22no—
1405C4—22no—
1406C4—28no—
1407C4—24no—
1408C4—24no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4—44no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4—42no—
1419C4—42no—
1420C4#342814yes—
1421C2—24no—
1422C2—44no—
1423C2C2×#342811yescharacteristic
1424C2C2×C4×2−1+411yescharacteristic
1425C2#6265311yescharacteristic
1426C2#6294012yes—
1427C2#6295012yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#121C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #34505C2semidirect
3. #34490C2semidirect
4. #34490C2semidirect
5. #34488C2semidirect
6. #34475C2semidirect
7. #34475C2semidirect
8. #34465C2semidirect
9. #34463C2semidirect
10. #34459C2semidirect
11. #34455C2semidirect
12. #34445C2semidirect
14. #34389C2semidirect
15. #34334C2semidirect
16. #34314C2semidirect
17. #34297C2semidirect
18. #34286C2semidirect
19. #34262C2semidirect
20. #34254C2semidirect
23. #34221C2semidirect
24. #34215C2semidirect
26. #34145C2semidirect
27. #34128C2semidirect
28. C4×#541C2semidirect
29. C2×#2320C2semidirect
30. #3523C4semidirect
262. #557C2×C4semidirect
263. #557C2×C4semidirect
264. #557C2×C4semidirect
265. #556C2×C4semidirect
266. #556C2×C4semidirect
267. #552C2×C4semidirect
268. #552C2×C4semidirect
269. D4×Q8C2×C4semidirect
270. D4×Q8C2×C4semidirect
271. #541C2×C4semidirect
272. #541C2×C4semidirect
273. #533C2×C4semidirect
274. #533C2×C4semidirect
310. #519C2×C4semidirect
311. C2×C4×Q8C2×C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35232
#345052
#344902
#344882
#344752
#344652
#344632
#344592
#344552
#344452
#343902
#343892
#343342
#343142
#342972
#342862
#342622
#342542
#342412
#342342
#342212
#342152
#341492
#341452
#341282
C4×#5412
C2×#23202